展开 (2(a+h)^2-5(a+h)+1)/h

解答

展开

\frac{2 ( a + h ) ^{2} - 5 ( a + h ) + 1}{h}

\frac{2 a ^{2}}{h} + 4 a + 2 h - \frac{5 a}{h} - 5 + \frac{1}{h}

求解步骤

\frac{2 ( a + h ) ^{2} - 5 ( a + h ) + 1}{h}

(a + h)^{2} = a^{2} + 2 ah + h^{2}

= \frac{2 ( h ^{2} + 2 ah + a ^{2} ) - 5 ( h + a ) + 1}{h}

乘开

2 (a^{2} + 2 ah + h^{2}) - 5 (a + h) + 1 : 2 a^{2} + 4 ah + 2 h^{2} - 5 a - 5 h + 1

= \frac{2 a ^{2} + 4 ah + 2 h ^{2} - 5 a - 5 h + 1}{h}

使用分式法则:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{2 a ^{2} + 4 ah + 2 h ^{2} - 5 a - 5 h + 1}{h} = \frac{2 a ^{2}}{h} + \frac{4 ah}{h} + \frac{2 h ^{2}}{h} - \frac{5 a}{h} - \frac{5 h}{h} + \frac{1}{h}

= \frac{2 a ^{2}}{h} + \frac{4 ah}{h} + \frac{2 h ^{2}}{h} - \frac{5 a}{h} - \frac{5 h}{h} + \frac{1}{h}

消掉

\frac{4 ah}{h} : 4 a

= \frac{2 a ^{2}}{h} + 4 a + \frac{2 h ^{2}}{h} - \frac{5 a}{h} - \frac{5 h}{h} + \frac{1}{h}

消掉

\frac{2 h ^{2}}{h} : 2 h

= \frac{2 a ^{2}}{h} + 4 a + 2 h - \frac{5 a}{h} - \frac{5 h}{h} + \frac{1}{h}

消掉

\frac{5 h}{h} : 5

= \frac{2 a ^{2}}{h} + 4 a + 2 h - \frac{5 a}{h} - 5 + \frac{1}{h}

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